Editing Meantone temperament (section)

===Equal temperaments===

In neither the twelve tone equitemperament nor the quarter-comma meantone is the fifth a [[rational number|rational]] fraction of the octave, but several tunings exist which approximate the fifth by such an interval; these are a subset of the [[equal temperament]]s {{nobr|( "{{mvar|N}} {{sc|TET}}" ),}} in which the octave is divided into some number ({{mvar|N}}) of equally wide intervals.

Equal temperaments that are useful as approximations to meantone tunings include (in order of increasing [[Generated collection|generator]] width) {{nobr|[[19 equal temperament|19 {{sc|TET}}]]}} {{nobr|({{sfrac| ~ | 1 | 3 }} comma),}} {{nobr|50 {{sc|TET}}}} {{nobr|({{sfrac| ~ | 2 | 7 }} comma),}} {{nobr|[[31 equal temperament|31 {{sc|TET}}]]}} {{nobr|({{sfrac| ~ | 1 | 4 }} comma),}} {{nobr|43 {{sc|TET}}}} {{nobr|({{sfrac| ~ | 1 | 5 }} comma),}} and {{nobr|55 {{sc|TET}}}} {{nobr|({{sfrac| ~ | 1 | 6 }} comma).}} The farther the tuning gets away from quarter-comma meantone, however, the less related the tuning is to harmonic ratios. This can be overcome by [[dynamic tonality|tempering the partials]] to match the tuning, which is possible, however, only on electronic synthesizers.<ref>
{{cite journal
 | last1 = Sethares | first1 = W.A. | author1-link = William Sethares
 | last2=Milne      | first2 = A.       | last3=Tiedje    | first3 = S.
 | last4=Prechtl    | first4 = A.       | last5=Plamondon | first5 = J.
 | year = 2009
 | title = Spectral tools for dynamic tonality and audio morphing
 | journal = [[Computer Music Journal]]
 | volume = 33  | issue = 2  | pages = 71–84
 | citeseerx = 10.1.1.159.838  | s2cid = 216636537
 | doi = 10.1162/comj.2009.33.2.71
 | id = {{Project MUSE|266411}}
}}
</ref>

[[File:Meantone_fifths_vs_thirds_comparison.svg|800px|thumb|center|Comparison of perfect fifths, major thirds, and minor thirds in various meantone tunings with just intonation]]
<br />
{{Center | '''Approximation of just intervals in equal temperaments'''<br />{{Gallery items | itemalign="center" | captionalign="center"
| [[File:12ed2-5Limit.svg|150px|thumb|center]] | 12-ET
| [[File:19ed2.svg|150px|thumb|center]] | 19-ET
| [[File:31ed2.svg|150px|thumb|center]] | 31-ET
| [[File:43ed2.svg|150px|thumb|center]] | 43-ET
| [[File:50ed2.svg|150px|thumb|center]] | 50-ET
| [[File:55ed2.svg|150px|thumb|center]] | 55-ET
}}}}